Question 215359
The diagonal of a square is 26 inches. Find the length of a side and the perimeter.


Step 1.  We'll use the Pythagorean Theorem which states that the sum of the  square of the sides or legs of a right triangle is equal to the square of the hypotenuse or {{{c^2=a^2+b^2}}} and for this example, c is the diagonal and a=b is the side since it's a square.


Step 2.  So with a=b then {{{c^2=a^2+a^2=2a^2}}} or c=a*sqrt(2).


Step 3.  Since c=26 inches then {{{a=c/sqrt(2)=26/sqrt(2)=13*sqrt(2))}}} or {{{a=18.38}}} inches.


Step 4.  Perimeter P means that we add up all the form sides or {{{P=4a=4*13sqrt(2)=52sqrt(2)}}} or P=73.39 inches.


Step 5.  The side is 18.38 inches and the perimeter is 93.39 inches.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J